2x + 3/ x - 4 - 2x - 8/ 2× + 1 = 1

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28-08-2016
Mathematics

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2x + 3/ x - 4 - 2x - 8/ 2× + 1 = 1

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dalendrk dalendrk · Answer 1 · 2016-08-28T02:33:13+02:00

[tex]\dfrac{2x+3}{x-4}-\dfrac{2x-8}{2x+1}=1\ \ \ |the\ domain\ D:x\neq4\ and\ x\neq-\dfrac{1}{2}\\\\\dfrac{(2x+3)(2x+1)}{(x-4)(2x+1)}-\dfrac{(2x-8)(x-4)}{(2x+1)(x-4)}-1=0\\\\\dfrac{4x^2+2x+6x+3}{2x^2+x-8x-4}-\dfrac{2x^2-8x-8x+32}{2x^2+x-8x-4}-\dfrac{2x^2+x-8x-4}{2x^2+x-8x-4}=0\\\\\dfrac{4x^2+8x+3}{2x^2-7x-4}-\dfrac{2x^2-16x+32}{2x^2-7x-4}-\dfrac{2x^2-7x-4}{2x^2-7x-4}=0\\\\\dfrac{4x^2+8x+3-2x^2+16x-32-2x^2+7x+4}{2x^2-7x-4}=0\\\\\dfrac{31x-25}{2x^2-7x-4}=0\iff31x-25=0\\\\31x=25\\\\\boxed{x=\frac{25}{31}}[/tex]